NBER 1orking Paper Series

THE EFFECT OF MINIMUM WAGE LEGISLATION ON

INCOME EQUALITY: A THEORETICAL ANALYSIS

J. Huston McCulloch

Working Paper No. 171

CENTER FOR ECONOMIC ANALYSIS OF HUMAN BEHAVIORAND SOCIAL INSTITUTIONS

National Bureau of Economic Research, Inc.204 Junipero Serra Boulevard, Stanford, CA 94305

March 1977(revised)

Preliminary; not for quotation.

NBER working papers are distributed informally and in limitednumber for coents only. They should not be quoted withoutwritten permission of the author.

This report has not undergone the review accorded officialNBER publications; in particular, it has not yet been submittedfor approval by the Board of Directors.

The author is Scherman Research Fellow at NBER—West, andAssistant Professor (on leave) in Economics at Boston College.He is indebted to Lee K. Benham and James R. Meginniss forhelpful coents and suggestions.

ABSTRACT

Minimum wage legislation is frequently advocated in the belief that it

creates a more nearly equal distribution of income. A one—sector model of

general equilibrium is used to analyze a universally applicable minimum

wage, and a two—sector mQdel is used to analyze a minimum wage that is

only applied to certain industries. In both cases we find that a minimum

wage may well lower equality (as computed by the Gini index) if we consider

reasonable values for the parameters of these two models. In the absence

of unemployment compensation, equality can increase only if the elasticity

of substitution in production is quite low. In the one—sector case, how-

ever, equality necessarily rises if unemployment compensation is present

and sufficiently generous.

1

INTRODUCTION

Minimum Wage legislation is frequently advocated in the belief that

it creates a more nearly equal distribution of income. In this paper we

investigate the positive economic question of the conditions under which

this belief is true. We find chat whether it is true depends on whether

the minimum wage is universally applicable, and in the case of a universally

applicable minimum wage, on the level of unemployment compensation.

In general we find that a legal minimum wage will actually reduce

income equality, unless the elasticity of substitution in production between

low—wage labor and other factors of production is fairly low, or unemploy-

ment compensation is sufficiently generous.

By investigating this issue, we do not mean to suggest that income

equality is necessarily desirable or equitable. Indeed, Robert Nozick

(1974, chapter 7) has recently demonstrated that distributive justice does

not require any particular state of income or wealth distribution, but

rather a process by which the economy moves from one state to another. In

other words, the proper criterion of justice does not ask how much an

individual has, but rather how he acquired what he has. Greater equality

can therefore actually be inequitable, depending on how the increase in

equality comes about. Nevertheless, the effect of a minimum wage law on

equality is an interesting economic question, to the extent that those who

advocate it regard equality as desirable (Mises 1963, 858).

In this paper, we measure equality with the Gini index, the ratio of

the area under the Lorenz curve to the area under the 45 degree line that

2

represents perfect equality (Gini 1921). This index is, admittedly,

open to objections detailed by Newberry (1970). An alternative class of

indices has been proposed by Atkinson (1970). However, for many values

of Atkinson's parameter e , his index registers perfect inequality if

even one person reports zero income. The Gini index, on the other hand,

is capable of differentiating between different percentages of the population

reporting no income. Since the Gini index is also easily computed and

familiar to economists, we will make do with it.

A ONE-SECTOR MODEL

First, we consider the effects of a universally applicable minimum

wage law, in a one—sector economy. For the sake of simplicity, we will

assume that there are two homogeneous factors, unskilled labor U and skilled

labor S , who between them comprise the entire population, and that output

X is produced competitively by means of a constant returns to scale

production fucntion X = F(U, S). To simplify the analysis, we will ignore

the supply elasticities of U and S , as well as mobility between the two

groups.

We could instead couch our analysis in terms of "Labor" and "Capital."

However, since wages and salaries constitute the great majority of national

income, it seems more relevant to distinguish between different types of

labor that between labor and capital. If the reader is concerned about

non—labor factors, he may consider them within the context of the present

model as being owned uniformly by the "skilled laborers."

Although in theory our competitive analysis would have to be modified

if employers are able to exert monopsony power, in practice few labor

3

markets are sufficiently concentrated to permit such power (Bunting 1962,

3—14). Furthermore, even in the presence of monopsony power, a simple

minimum wage is unlikely to do much to produce the efficiency gains and

expanded employment that are possible in theory (Stigler 1946).

Let W aLd W be the wage rates paid to unskilled and skilledU S

labor respectively, taking the price of X as numeraire. Let k = IJW/X and

1—k = SW /X be the relative shares of U and S in national income. WeS

measure U and S as fractions of the total population, so that U + S = 1

initially, when there is full employment.

The Lorenz curve in the absence of a minimum wage law is shown in

Figure 1.1 In this diagram, the entire population is arranged along the

horizontal axis from the lowest income individuals (the unskilled laborers)

to the highest income individuals (the skilled laborers). The vertical

axis measures percent of total income earned by individuals to the left of

any given value on the horizontal axis. Our initial Lorenz curve follows a

straight line from the point (0, 0) to (U, k), and then another straight

line to (1, 1).

Suppose now that a universally applicable and completely effective

minimum wage law is passed, preventing laborers from working (or what

amounts to the same thing, preventing employers from hiring them) if they

cannot cotand a certain minimum wage somewhat higher than the market

unskilled wage, say W + dW . This law will throw unskilled workers outU U

of work until the marginal product of those remaining equals the minimum

wage. To the extent that workers embody human capital that is specific

11n this paper we assume away life—cycle earnings patterns that generallycause transitory income to be less equally distributed than the morerelevant concept of total human wealth (discounted lifetime earnings).See Lillard (1977).

Percent of Population

FIGURE 1Initial Distribution of Incomein 1—Sector Model.

Percent of Population

FIGURE 2Income Distribution in 1—Sector Model with MinimumWage and a > 1.

Percent of Population

FIGURE 3Income Distribution in 1—Sector Model with MinimumWage and a c 1.

FIGURE 4Demand Curve for U.Product Curve.)

(Marginal

4

1—1-k-dk

k

I U SI

k+dk

U+dU S

a)

a00H

0

C.)

p..

WU

dWU

0

1-k-dk

D

k+dk

-dUl U + dUI I dU U

5

to the firm they work for (such as hiring costs or specific training),

the unemployment effect will be lessened in the short run. (See Oi 1962.)

However, in the long run the full unemployment will appear. In any case,

unskilled workers probably embody relatively little human capital, specific

or otherwise, so that there will be substantial unemployment even in the

short run. Thus, Brozen (1969) and Kosters and Welch (1972) find appreciable

short—run unemployment effects among teen—agers, and especially among

non—white teen—agers. We therefore believe our simple model captures a large

part of the truth.

In the absence of unemployment compensation, the unemployed make nothing,

so they are now at the very bottom of the income distribution, even below

the employed unskilled. The total share of unskilled, unemployed and employed

together, is now k + dk. It is well known (and will be demonstrated below

in passing) that dk will be negative if the elasticity of substitution

(Hicks 1957, 245) between the two factors is greater than unity, and

positive if it is less than unity. In the former case, illustrated in Figure

2, the new Lorenz curve will, be entirely below the original curve, so that

equality surely must decline by any measure. In the latter case, however,

the new Lorenz curve starts off below the original curve and then passes

above it, as shown in Figure 3. It is not at once obvious whether equality

has risen or fallen in this case.

In order to solve this problem we must explicitly compute the Cmi

index. Its initial value is

C = [-kiJ += kU + (k+1)S

=k+S . 1)

6

Keeping in mind that dU is negative, the value of the Gini index as

modified by the minimum wage law is

G+dG= [(k+dk)(u+du) +(k+dk+l)S]/= kU + kdU + Udk + dkdU + kS + Sdk + S

= G + dk + kdTJ + dkdU

The term dkdU is of only the second order of smalls, so we may ignore it if

dW is sufficiently small:

dG=dk+kdU . 2)

The demand curve for U will be the schedule of the marginal product

of U given the quantity of S available, that is, F(U, S). When Wgoes up by dWu , U falls by dU (see Figure 4). The slope of this curve

is F, the second partial derivative of F with respect to U, so we have

dW/dU=FU UU

By Euler's theorem we have UP + SF = 0 , so thatuU US

dU/dW = —U/(SF )U US

= — [U/WI [x/ (SW) I [FF/ (XF) 1

= —Ua/[W (1 — k)]U

EU —ciEW/(l — k) , 3)

where = F F /(XF ) is the elasticity of substitution between U andus us

S , W = F and W = F are the marginal products of U and S , and "E"U u S s

represents the logarithmic differentiation operator:

7

EU d in U

= dU/U, etc.

Differentiation of X = F(U, S) gives

dX = F dU + F dSU S

= W dUU

EX=kEIJ. 4)

We also have

dk d(UW/X)

= k(EU + EW - EX)U

= k[EW + (1 - k) EU]

=k (l—) EW . 5)

Equation 5) shows us why must be less than unity for the mimimuxn

wage law to raise the relative share of U. Since the unmployed receive

nothing, k (or k + dk) is at once the share of employed U and the share

of all U . Substituting 3) and 5) into 2), we have

dG = [k(l — ,) — kaU/(l — k)] EWU

= k[(l— k) — (l + U — k)] EW 1(1 — k) . 6)U

Equation 6) implies that "equality," at least as reckoned by the Gini. index,

will rise if and only if

8

1-k0< 7)1 + U—k

The expression (1 — k)/(l + U — k) is always less than 1 — k, since

the income share k of unskilled workers is necessarily less than their

population share U. Therefore a would have to be fairly low, in com-

parison to the remarkably robust Cobb—Douglas value of unity (Douglas 1976),

for equality to increase) For example, if unskilled are half the population

and make half as much as skilled workers, we will have

UWk= u13W + SWu S

.25 W= U

.25 W +.5WS S

13,

and2

1-k - 31+13-k 123

47,

laufman and Foran (1968/71, 189—218) erroneously investigate theshare of the affected factor in order to determine whether or not thelegislation has increased equality. We have shown that if (1—k)/(1+U—k) <a < 1, equality will fall even though the share of the directly affectedfactor rises.

Zucker (1973) finds estimates of the demand elasticity for low—wagelabor between —0.79 and —1.15. By (3), the elasticity of substitutiontherefore would lie between .79(1—k) and 1.15(1—k), which is probably belowunity, in spite of the apparent robustness of the Cobb—Douglas formulation.

9

so that a would have to be less than 4/7 for equality to rise.

The percentage change in the absolute share of unskilled labor is given

by

E(UW ) EU + EWU U

= [1 — a/(l — k)] EW

This quantity is positive for a rise in W if and only if a < (3. — k)

Since we must have (1 — k)/(l + U — k) < (1 — k) < 1, we may state that a

minimum wage law will raise equality only if it raises the absolute share of

U, and it wil]. raise the absolute share of U only if it raises the relative

share of U

It might be objected to the analysis of this section that the unemployment

will rotate among the directly affected group of workers, so that there will

not, in the long run, be an identifiable class of unemployed. In this case, it

would only be necessary for a to be less than 1 (a much more likely event

than a < (1 — k]/[l + U — k]) for equality to increase. However, this

objection confuses frictional unemployment with minimum wage unemployment. As

a rule, we would expect.unemployment caused by ordinary job turnover to pass

from worker to worker, while that caused by minimum wage legislation would not.

If there is even the slightest difference in the efficiency of different

unskilled workers, the burden of minimum wage unemployment will fall entirely

on the shoulders of the least efficient. Thus the resulting unemployment will

persistently afflict the already otherwise disadvantaged: the unschooled, the

inexperienced, teenagers, and those who have not mastered the majority language.

10

Even if efficiency is uniformly distributed, the available jobs are likely

to be rationed by employers on the basis of non—efficiency considerations

that would ordinarily be overridden by market forces, such as race, religion,

sex, ethnic origin, political affiliation, or kinship.

We therefore must conclude that although it is not impossible for a

universally applicable minimum wage to increase the equality of income dis-

tribution in the absence of unemployment compensation, it is not very likely

to do so. In the event that it does actually raise equality, it is only

because the improved position of employed unskilled labor relative to skilled

labor outweighs the necessarily deteriorated position of unemployed unskilled

relative to employed unskilled. In any event there is always increased

inequality at the lower end of the income distribution.

11

THE ONE—SECTOR MODEL WITH UNPLOYMENT COMPENSATION

In the presence of unemployment compensation, the effect on equality

of a universally applicable minimum wage law will be somewhat different.

Suppose that the unemployed are compensated at the fraction a of the wage they

would obtain if they were employed, so that they receive aW . (Whether they

receive aW , a(W + dW ), or a(W + dW )(l — t) will not affect the resultsU U U U U

below, so long as dW is infinitessimal.) Although such compensation can

act as a strong subsidy to unemployment (Feldstein 1974), we will ignore these

supply effects, and assume that observed employment is affected only by the demand

effect of a minimum wage, provided a is less than unity.

We will assume that the compensation is paid for out of a proportional

income tax. While such a tax is likely not to be proportional in practice,

we make this assumption in order to investigate the distributional effects of

the minimum wage with unemployment compensation in isolation from the effect

of redistributive tax structures.

The unemployed receive _aWdU, and output becomes X+dX (where both dU

and dX are negative), so the income of the employed unskilled and skilled

workers must be taxed at the following rate in order to finance the corn—

pensation:

-aW dUU

X+dX

Ignoring terms in the second order of smalls, this rate becomes

12

t = —akEU

With unemployment compensation, the Lorenz curve in the presence of

a minimum wage law will pass from (0, 0) to (—dU, —akEU) to (U, k+dk) to

(1, 1), where we interpret k+dk as the modified share of all unskilled

workers, including the unemployed. The new Gini index is now

G + dG =[akETJdU + (U +dU) (-akEU + k + dk)

++(1+k+dk)S1/4

Ignoring terms in the second order of sinalls and rearranging, we have

dG (l—a)kUEU + dk

The modified after—tax share of unskilled workers is now

-aW dU + (U+dU) (W +dW ) (1+akEU)k + dk =

x(1+EX)U U

8)

Again ignoring terms in the second order of smalls and rearranging, we have

dk = k(l—k)(l—a)EU + kEW

=k(l—(1—a))EWU

so that

dG —(1—a)k U=

1—k+ k(l — (1 — a))

= [1 - k - (1 - a)u(1 + U - k)1 9)

13

This expression is positive if and only if

1—k

(l—a)(1+U—k)

If a is between zero and unity, we see that if a is small enough to

increase equality without compensation, it is necessarily small enough to

increase equality with compensation.

We also see that the more generous unemployment compensation is, the more

likely a minimum wage is to increase equality. In particular, as the fraction a

approaches unity, a universally applicable minimum wage becomes certain to

increase equality.

It does not follow, however, that generous unemployment compensation

necessarily increases the income of unskilled workers. Their total after

tax income N+dN is the numerator of the right—hand side of (8). Once

more expanding and ignoring terms in the second order of smalls, we have

dN = U[l — a(l+ak—a)1 dW . 10)u 1—k u

Unskilled labor income therefore rises if and only if

1—kl+ak—a

or equivalently,

a>a (1—k)

Since a is bounded by zero and unity, we see that if a is less than 1—k,

14

unskilled income necessarily rises, even if a equals zero. On the other

hand, if a is greater than (l—k)/k, unskilled income necessarily falls,

regardless of a.

15

A TWO—SECTOR MODEL

Most minimum wage legislation is not universally applicable as we have

assuaed above. Although less qualified workers are effectively barred from

certain occupations, other occupations may remain open to them. Usually these

uncovered jobs are in fields such as agriculture, domestic service, small—

scale industry, and self employment. If the displaced workers prefer low—pay

jobs in these fields to unemployment, the effects of the minimum wage law will

be modified.2 In this section, we will ignore the possibility of unemploy-

ment compensation, in effect assuming that unemployment compensation is

unattractive in comparison to employment in the low—wage uncovered sector.

Let us assume that there are two sectors, producing outputs X and Y

competitively. Let m be the share of the X—industry in national income and

let f and g be the shares of unskilled labor in the income of the X and

Y sectors respectively. Let U , U , S , and S be the quantities ofx y x y

unskilled and skilled labor used in the two industries, measured as fractions

of the total labor force (again taken to be the entire population), so that

U + U + S + S = U + S = 1 . Take the salaries of the skilled workers asx y x y

the numeraire, and let W and W be the wage rates for unskilled workers inx ythe two industries. Initially, W =

WY= W < 1

2See Brozen (1962) for an analysis of the stimulating effect minimumwage rises have on the pool of domestic workers. Dropping out of the laborforce altogether to perform non—market household duties or leisure activitiesmay also be interpreted as entering an uncovered industry. Thus, Moore (1971)finds that the increase in the minimum wage in .1961 seems to have lowered

the subsequent labor force participation of teenagers. We assume job turnover

in the covered sector to be low enough that speculative unemployment of thetype Mincer (1976) dIscusses does not appear.

3Th1s model is essentially that employed by Jones (1965), Johnson (1969) andJohnson and Mieszkowskj (1970). See McCufloch (1974) and the comments below,however, for qualifying considerations in a special case.

16

Let N be national income (P X + P y) and k, k , and k be thex y x y

shares of U, U , and U in N. We then must havex y

k = W U INx xx

mf 11)

k =WU/Ny yy= (1—m)g 12)

k=k +kx y

m1+ (l—m)g . 13)

Figure 5 shows the initial distribution of income, before the minimum

wage is applied. In Figure 6, a minimum wage has been applied to the X sector,

raising the real wage in that industry, both absolutely and relative to the

wage in Y . Instead of unemployment appearing, we assume now that unskilled

laborers are perfectly mobile so that those displaced by the minimum wage

immediately find work in the uncovered Y sector.

The initial value of the Gini index of equality is, as before,

G=k+s

After the minimum wage is introduced, we have

C + dG = [-(U -dU ) (k +dk ) + (U +dU ) (k +dk +k+dk +dk )2y x y y 2 x x y y y x

+ S(l+k+dk -+-dk )]/-

0

0C.)

'-4

4-404-)

C.)

FIGURE 5Initial Distributionin 2—Sector Model.

of Income

Percent of Population

FIGURE 6Income Distribution in 2—Sector Model with Minimum

Wage. (Drawn as if shareof U falls.)

17

1—k80C.)

-4

kx

ky

I 'U ISy x

Percent of Population

1-k-dk

x-dk

y

kx

+dk-ry

I U —dU sI y dU

x

18

Rearranging, ignoring terms in the second order of smalls, and using

U k = U k , we obtainxy yx

dG=kdU +(1+U)dk +(S+U)dkx x y x x

Now

dk = k [(1—k)EW + EU + (1—k )E(W 1w )]x x y x x x y

dk = k [(1—k)EW — (U IU )EU — k E(W 1W )]y y y xy x x xy

whence

dG = k(1—k) EW + k (1 - k — U ) E(W 1w ). 14)y x x xy

We assume that the owners of both factors have the same marginal

propensity to consume each of the two goods so that redistributional effects

have no influence per se on the output mix. Let be the elasticity of

substitution in consumption between X and Y, and a and a be thex y

elasticities of substitution in production between U and S . (These

substitution elasticities are defined so as to be positive.) Then following

Harberger,4 we have the following system of equations relating small changes

in W , S , U, and W/Wy x x xy

4Harberger (1962, 226—7). We have substituted —(l—m)a for Harberger'sdemand elasticity E, U for his "capital," and S for his "labor."

19

(_(1_m)af \ ( (1—m)a(f—g) 1—f f \ / EW\0

\E(W/W) = —(1—m)ag(l—g) —m(l—f)g mf(1_g)\) ES 15)

- / a -1 1 / \ EU /

The determinant of this system,

D = m(1_m)a(f_g)2 + (l-m)ag(1-g) + maf(1_f) > 0

is always positive. Using Cramer's rule, we have

D y = — mf[(1—in)a (f—g) + a (1—f)] , 16)E(W/W)

C Xxyso that

D dG = m(l—m)a (f—g)[k (1—k—U )(f—g) — k(l—k)f]E(W/W)

C X Xxy+ ma f(1—f)[—k U — k (1—k)] 17)x xx y

+ (1—m)ag(1—g)k(1—k—U).

This formula is valid to the extent that system (15) is valid. However,

in another paper (NcCufloch 1974) we have shown that if a is sufficientlyC

large in comparison to a and a , and the covered X industry is labor—

intensive, this system is invalid, since a minimum wage in the X industry,

even when dW is infinitessimal, will result in a discrete change in the

employment and output variables, rather than the irifinitessitnal changes

assumed by the equations. This problem arises when

(l—m)g[ma(l—f)(g—f) + a (l—g)(1.-mf) + maf(l—f)]/D, 18)

20

which according to system (15) is the value of (EW —EP)/(EW —EW), is

negative.5 When expression (18) is negative, a minimum wage in the X

industry will cause a discrete reduction in X output and employment and

may even close down the X industry. We have made no assumptions about how

the economy behaves outside a small neighborhood of the initial equilibrium,

so we cannot say for certain what will happen to equality in this case.

However, it seems likely that it will decline.

Expression (17) can have either sign, depending on the values of the

underlying parameters. The term in is always negative, so that if in

or is large enough, equality will surely fall. Since it is the only one

of the three terms that is determinate in sign, equality tends, if anything,

to fall in the two sector model, though this is at best a weak presumption.

In order to obtain a better feel for the likely effect of a minimum wage

in this model, we assign prior probability distributions to the values of the

basic parameters and compute a derived prior probability that the minimum

wage will reduce equality. To be sure, the derived prior will depend

critically on the assumed parameter priors. Nevertheless, this is a convenient

way to summarize our knowledge of a complex expression, one which could perhaps,

with experience, be applied to other problems as well.

The parameters f, g, m, and W may take on values between 0 and 1, so we

will consider the five values .1, .3, .5, .7, and .9 for these four parameters.

5mis expression is the same as the right hand side of equation (14) onp. 447 of Jones (1971), in the case of an infinitessimal distortion.Jones, however, does not recognize the inapplicability of the differentialmodel when this expression is negative.

21

The substitution elasticities a , a , and a may take on values fromc x y

o to infinity. Estimates of substitution elasticities often cluster about

unity, so we will want to center our substition elasticity distributions

around 1. The range .5 to 2 probably includes most reasonable estimates of

the a's, but since (17) is sensitive to extreme values of these three

parameters, we will also include .1 and 10. Thus we consider the five

values .1, .5, 1, 2, and 10 for each of the three substitution elasticities. In

order not to give too much weight to the extreme values of the seven basic

parameters,6 we assign prior probabilities of .1, .2, .4, .2, and .1 to the

five values of each parameter, respectively. Assuming independence between the

prior distributions of our parameters we can then easily compute the prior

probability of each of the 57 = 78,275 combinations of values. Expression

(17) was evaluated for each of these combinations, resulting in a derived

prior probability of .799 that equality will fall. (When expression (18) proved

negative, it was assumed that equality would fall regardless of the value of

(17). However, this perverse case only occurred with prior probability .015,

so its treatment did not have a major effect on the results.)

In order to test the sensitivity of the change in the Cmi index to the

extreme values of .1 and .9 that we allowed for f, g, in, and W and of .1 and

10 that we allowed for a , a , and a , we also tried assigning the prior dis—C X y

tribution 0, .25, .5, .25, and 0 to the five values of each of the seven

bdsic parameters. In effect, this eliminated the extreme values. In this

6U may be calculated from in, f, g, and W using (11), (13), and

U = k[W + k(l-W)].

22

case expression (18) was never negative, and the derived prior probability

of equality falling rose to .906.

The effect on income equality of a minimum wage law that is not

universally applicable depends on the technological characteristics, importance,

and factor intensities of the covered and uncovered sectors. This will vary

with the provisions of the particular legislation under consideration. However,

we may conclude that it would take a fairly unusual combination of parameters

to prevent such a minimum wage from reducing income equality.

23

REFERENCES

Atkinson, A.B, "On the Measurement of Inequality," Journal of Economic

Theory 2:244—63, 1970.

Bunting, Robert L., "Concentration and Monopsony in Labor Markets" in Bunting,R.L., Employer Concentration in Local Labor Markets (University of NorthCarolina Press, 1962), pp. 3—14. Reprinted in Burton et al. (1971), 132—139.

Brozen, Yale, "Minimum Wage Rates and Household Workers," Journal of Law andEconomics 5:103—9, October, 1962.

____________ "The Effect of Statutory Minimum Wage Increases on Teen—AgeEmployment," Journal of Law and Economics 12(1):l09—22, April, 1969.

Burton, J.L., L.K. Benham, W.M. Vaughn, and R.J. Flanagan, eds., Readings inLabor Market Analysis (New York: Holt, Rinehart & Winston, 1971).

Douglas, Paul H., "The Cobb—Douglas Production Function Once Again: ItsHistory, Its Testing, and Some Empirical Values," Journal of Political

Economy 84 (October 1976), 903—916.

Feldstein, Martin, "Unemployment Compensation: Adverse Incentives and Dis-tributional Anomalies," National Tax Journal 27 (June 1974), 231—44.

Cmi, Corrado, "Measurement of Inequality of Incomes," Economic Journal 31:

124—6, March, 1921.

Harberger, Arnold C., "The Incidence of the Corporation Income Tax," Journalof Political Economy 70(3):215—40, June, 1962.

Hicks, John R., The Theory of Wages, 2nd. ed. (Gloucester, Mass.: Peter

Smith, 1957).

Johnson, Harry G., "Minimum Wage Laws: A General Equilibrium Analysis,"Canadian Journal of Economics 2(4):599—604, November, 1969.

Johnson, Harry C. and Peter Mieszkowski, "The Effects of Unionization on thethe Distribution of Income: A General Equilibrium Approach," QuarterlyJournal of Economics 84(4):539—61, November, 1970.

Jones, Ronald W., "The Structure of Simple General Equilibrium Models,"Journal of Political Economy 73 (December 1965), 557—572.

________________ "Distortions in Factor Markets and the General Equilibrium Modelof Production," Journal of Political Economy 79 (May/June 1971), 437—59.

24

Kaufman, Jacob J. and Terry G. Foran, "The Minimum Wage and Poverty," inTowards Freedom from Want, edited by S.A. Levitan, W.J. Cohen, andR. Lampman (1968), pp. 189—218. Reprinted in Burton et al. (1971),508—523.

Kosters, Marvin and Finis Welch, "The Effects of Mini-mum Wages on the

Distribution of Changes in Aggregate Employment," American Economic Review42(3): 323—32, June, 1972.

Lillard, Lee, "Inequality: Earnings vs. Human Wealth," American EconomicReview, March, 1977 (forthcoming).

McCulloch, J. Huston, "The Effect of a Minimum Wage Law in the Labour—Intensive Sector," Canadian Journal of Economics 7 (May 1974), 316—319.

Mincer, Jacob, "Unemployment Effects of Minimum Wages," Journal of PoliticalEconomy 84 (August, 1976, supplement), S87—S104.

Mises, Ludwig von, Human Action: A Treatise on Economics. Second edition.(New Haven: Yale, 1963).

Moore, Thomas Gale, "The Effects of Minimum Wages on Teenage UnemploymentRates," Journal of Political Economy 79(4):897—902, July/August, 1971.

Newberry, D., "A Theorem on the Measurement of Inequality," Journal ofEconomic Theory 2:264—5, 1970.

Nozik, Robert, Anarchy, State and Utopia (New York: Basic Books, 1974).

Ui, Walter Y., "Labor as a Quasi—Fixed Factor of Production," Journal ofPolitical Economy 70:538—55, December, 1962.

Rothschild, Michael and Joseph E. Stiglitz, "Some Further Results on theMeasurement of Inequality," Cowles Foundation Discussion Paper #344(unpublished). 1972.

Stigler, George J., "The Economics of Minimum Wage Legislation," American

Economic Review 36: 358—67, June, 1946. Reprinted in Burton et al. (1971).

Zucker, Albert, " Minimum Wages and the Long—Run Elasticity of Demand forLow—Wage Labor," Quarterly Journal of Economics 87 (May 1973), 267—277.